Overwatch is still in closed beta, which means that you'll need an invitation to get in. However, Blizzard is hosting the first ever Beta Test Weekend, and despite the fact that it won't be open to everyone, they will open up the game "to a lot more players from our Americas and Europe gameplay regions".
The stress test begins November 20th and runs through November 23rd. If you've been playing the closed beta since it kicked off it may be a good time to log in for some "easy kills", but playing for objectives may be somewhat frustrating at times given the influx of new players. Then again it's not rocket science, and most players will find their way quickly.